The use of Tikhonov regularization method for calculating the distribution function of relaxation times in impedance spectroscopy

Abstract

The state-of-the-art in realization of the method of distribution of relaxation times (DRT) as applied to the analysis of data of electrochemical impedance spectroscopy is briefly surveyed. The theoretical fundamentals of the DRT method are described, the methods of solving the Fredholm equation of the 1st order with respect to the unknown DRT function are considered as an ill-defined problem. The Tikhonov regularization method presently considered as the most suitable for solving this equation is discussed. For several numerical experiments, the high resolution of the DRT method and its stability with respect to noise in impedance spectra are demonstrated. Among the problems and limitations of the DRT methods, the choice of the optimal regularization coefficient is considered as the most significant. Particularly, it is shown that in those cases where several relaxation processes with the constant phase angle appear in the response of objects under study to ac disturbances, different regularization coefficients should be selected for each of these elements in order to obtain adequate results.